Dreyfus suggests further research needs to be conducted both by the analytical philosophers and the phenomenologists in order to better disclose how conceptual thinking arises from coping action and perceptual experience.

Given the availability of rich descriptions of perceptual
affordances and of everyday know-how, however, couldn’t analytic philosophers profit from
pursuing the question of how these nonconceptual capacities are converted into conceptual ones
— how minds grow out of being-in-the-world — rather than denying the existence of the
nonconceptual?

To demonstrate the subtlties of this question, he reviews how experts become experts, and what it means to act expertly. (See section IV of his APA presidential address.)

While infants acquire skills by imitation and trial and error, in our formal instruction we
start with rules. The rules, however, seem to give way to more flexible responses as we become
skilled. We should therefore be suspicious of the cognitivist assumption that, as we become
experts, our rules become unconscious. Indeed, our experience suggests that rules are like
training wheels. We may need such aids when learning to ride a bicycle, but we must eventually
set them aside if we are to become skilled cyclists. To assume that the rules we once consciously
followed become unconscious is like assuming that, when we finally learn to ride a bike, the
training wheels that were required for us to be able to ride in the first place must have become
invisible. The actual phenomenon suggests that to become experts we must switch from
detached rule-following to a more involved and situation-specific way of coping.

Indeed, if learners feel that they can act only if they have reasons to guide them, this
attitude will stunt their skill acquisition.

It's amazing, isn't it? Plato and (if Plato's to be believed) Socrates devoted much time to the question of whether certain things can be learned at all, and if so how they are learned. Plato's explanation was that the soul experiences things in their 'archetypal' Form, and that this results in innate (what we would probably now call a priori) knowledge which the perceiving being later simply 'recalls'.
Wittgenstein and Chomsky are also both among those who have examined the way in which rules correspond (or not) to the way we actually interpret perceived events.
I know some people's conclusion is that either these questions don't matter, or that if intellects like those above can't answer them, why should I fret about it... but to me they raise two questions which still fascinate:
First, can I understand what someone is getting at who has really, really thought hard about these questions?
Second, can I in any way relate their arguments and conclusions to my own experience and reasoning?
I may not ever reach definitive conclusions (let alone correct ones!), but I can't help but feel it's healthy to continute to question our in-built and accreted assumptions about stuff like this.

My understanding of Chomsky's work, or at least the essence of it, relates to his pursuit of one central question: Given the "poverty" of linguistic experience a child has, how is it possible for it to learn so much about the language he or she masters? To make his point, Chomsky gives examples of sentences which we have not heard before with grammatical subtlties that we have never been taught before—and yet, we can understand these sentences, and our sense of these sentences agree with the corresponding subtle grammatical points.

Chomsky concludes that we must have some innate faculties, which are tuned by the little experience we have for a particular purpose—in this case the mastery of a particular human language. He then explores whether the same mechanisms are involved in other sorts of mental faculties.

Of course, Chomsky is also interested in the syntactic structure of spoken language, but I don't think he believes that the child actually learns the rules. In fact, what drives his research is the fact that these rules cannot often be articulated by speakers, all of whom agree about the logical sense of a particular sentence. In a sense, and in accord with what Dreyfus wishes in his APA presidential address, Chomsky fits among the analytical philosophers who try to connect the foundation of perception with the higher, abstract modes of conception.

The question remains whether Chomsky believes the perceiving individual needs to grasp (i.e. think in the terms of) the higher level concepts in order to be able to cope with the world of language. It is this question, along with Chomsky's emphasis on logic and his early inspiration from Quine, that might set him widely apart from Dreyfus.

I would love to see Chomsky and Dreyfus to lead a seminar together, or at least their works to be presented side-by-side. The debates, the varying perspectives and concerns should lead to a great dialogue.

Chomsky argues that people have the ability to produce and understand new sentences that “are not similar to those previously heard in any physically defined sense …nor obtainable from them by any sort of “generalization” known to psychology and philosophy" (1965, p. 58). But it has been shown that generalizations based on acquired similarity standards (see, e.g., Quine 1974, p. 20) indeed account for grammatical competence.
Chomsky, N. (1965). Aspects of the theory of syntax. Cambridge, MA: MIT Press.
Quine, W.V. (1974). The roots of reference. La Salle, IL: Open Court.